Selecting Penalty Parameters of High-Dimensional M-Estimators Using Bootstrapping after Cross Validation
提出一种交叉验证后自助法，用于选择高维L1惩罚M估计量的惩罚参数，并证明其收敛速度，模拟显示在推断上优于交叉验证。
We develop a new method for selecting the penalty parameter for ℓ<sub>1</sub>-penalized M-estimators in high dimensions, which we refer to as bootstrapping after cross validation. We derive rates of convergence for the corresponding ℓ<sub>1</sub>-penalized M-estimator and also for the post-ℓ<sub>1</sub>-penalized M-estimator, which refits the nonzero entries of the former estimator without penalty in the criterion function. We demonstrate via simulations that our methods are not dominated by cross validation in terms of estimation errors and can outperform cross validation in terms of inference. As an empirical illustration, we revisit Fryer (2019), who investigated racial differences in police use of force, and confirm his findings.